If x⁴+1/(x⁴) = 34 where x > 0, then find the value of (x+1over x) .

If x⁴+1/(x⁴) = 34 where x > 0, then find the value of…

If $x^4+\frac{1}{x^4}$ = 34 where x > 0, then find the value of $(x+{1\over x})$ .

Show answer & explanation

Correct answer: C

Explanation

The correct answer is Option 3 i.e. $2\sqrt2$ .

$x^4+\frac{1}{x^4}$ = $(x^2+{1\over x^2})^2$ - 2

⇒ 34 = $(x^2+{1\over x^2})^2$ - 2

⇒ $(x^2+{1\over x^2})^2$ = 36

⇒ $(x^2+{1\over x^2})$ = 6

⇒ $(x^2+{1\over x^2})$ = $(x+{1\over x})^2$ - 2

⇒ 8 = $(x+{1\over x})^2$

⇒ $(x+{1\over x})$ = $2\sqrt2$